Could There Be a Topic Worse than Baseball? What about Math?

Did my column two weeks ago about baseball put off some readers? Yes. A dear friend, whom I’ve known my whole life, wrote: “Ya lost me at the topic.” That’s about as far from “You had me at ‘hello'” as it gets. What could be worse? Another dear friend, brought up in Brazil, unsubscribed from the newsletter. (Don’t get any ideas.)

Doomed to repeat the past rather than learn from it, I now want to talk about a topic even more visceral to some readers than baseball. I want to talk–briefly, I promise–about math.

Steven Hawking, who by all accounts knows more math than I do, relates in A Brief History of Time, that his publisher told him that every mathematical equation he used in the book would cost him a number of readers. So he only used one equation. I’ll do even better–no equations at all. And I promise I’ll make a point about parenting too.

But first, some simple math: Three people–Abercrombie, Bartholomew, and Clarissa–work together at an advertising agency. How many different ways can they make a presentation?

Well, they could all get up on stage together, all three of them. That’s one way.

Or, they could split up into groups of two as follows:

Abercrombie and Bartholomew

Bartholomew and Clarissa

Abercrombie and Clarissa

So, there are three of these “groups of two.”

Of course, they could just present individually. Abercrombie could take the stage alone. Or Bartholomew could. Or Clarissa. So that’s three more ways.

And lastly, they could just do a “ghost presentation.” No one could go up on stage. That would be a statement of some kind, I suppose. But nobody on the stage has to be counted as a unique way.

In total, there are eight different ways that three people can be grouped. One plus three plus three plus one equals eight.

But what if there were ten people instead of just three? What if we wanted to know how many different ways that ten people–Abercrombie, Bartholomew, Clarissa, Dysentery, Englebert, Felicity, Ganbaatar, Halcyon, Icarus, and Jagdesh–could make the presentation?

I don’t want to list all the possible groupings of ten people. I don’t even want to start thinking about whether or not I forgot to write down any of the groups of two. (There are 45 of these groups of two.) Never mind the groups of three–of which there are 120. There has to be a better way.

Which is where math comes in.

To figure out how many groups of three there are, just multiply two by itself three times. Two times two times two is eight. That’s the same eight we got by listing all the groups. (Not to be confused with two times three which is six.) Two to the third or 2 ^ 3, is eight.

To figure out how many groups there are with ten folks, we multiply two times itself a bunch more times. Two times two times two times two times two times two times two times two times two times two. Another way to say this is “two raised to the tenth power,” written 2 ^ 10. Two to the tenth power is just over a thousand. That’s a lot of different groups.

Now–finally you might say–comes the parenting part. I met with the family of a high school student the other day. The young man was taking ten different medications. He was taking a psycho-stimulant for attentional issues. He was taking a selective serotonin reuptake inhibitor (SSRI) for issues with depression and anxiety. He was taking an atypical anti-psychotic. He was taking a mood stabilizer. He was taking a benzodiazapine to help him sleep. He was taking four other medications, none of which I was familiar with. I seem to remember something about one medication being used to undo some side effect of two of the other medications. (Anyone remember all the verses to “I know an old woman who swallowed a fly”?)

Here’s my question. See if you can answer it based on what you learned about Abercrombie, Bartholomew, Clarissa, Dysentery, Englebert, Felicity, Ganbaatar, Halcyon, Icarus, and Jagdesh If a young man is taking ten different medications, how many different interactions are there between all those med’s? If you answered “1024”–the same “two to the tenth power” as before–you get full credit. If you answered, somebody needs to let this poor kid go out and play, you get an A+.